Throughout the movie Avengers: Infinity War there’s some relatable exchange between Thanos and Stark. Either they are talking to each other about each other or talking to others about each other.

At Doctor Strange’s sanctum where Banner is making everyone aware of what’s coming and Stark goes "Tell me his name again?"

At Ebony Maw’s spaceship while Tony and Strange are hatching a plan Tony says something on the lines of "I have been waiting for Thanos since 6 years since New York"

At Titan during the battle, Thanos identifies and calls out “ Mr Stark” to which Tony asks "You know me?" And Thanos responds "You’re not the only one cursed with knowledge"

To conclude, at the beginning Tony doesn’t know Thanos but later he says he’s been waiting for 6 years for this revenge and later Thanos recognises him. So do Thanos and Tony share parallel history and both are aware/unaware of each other?

I interpreted Thanos "knowing" Stark as a side effect of him wielding the Soul Stone, in the same way Red Skull was "cursed" to know everyone visiting the planet it was on (and how did he know that, if not through the Stone enforcing this?) Thanos may have known of Stark in general due to the events in Avengers being reported back to him, but he didn't truly know Stark until he was face to face with him and the Stone forced the knowledge upon him.
– Jeroen MostertMay 6 '18 at 13:25

1 Answer
1

At Doctor Strange’s sanctum where Banner is making everyone aware of
what’s coming and Stark goes "Tell me his name again?"

At this point Tony has no idea who or what Thanos is - he's learning about him for the first time, mostly from Bruce, who has had first hand experience of him. Bruce tells him that Thanos sent Loki to New York.

At Ebony Maw’s spaceship while Tony and Strange are hatching a plan
Tony says something on the lines of "I have been waiting for Thanos
since 6 years since New York

Tony has been waiting since the New York battle in Avengers for the next invasion. This is the whole motivation behind his creation of Ultron - a shield around the planet for the next invasion force be deflected by. Remember that Scarlet Witch showed him a vision of a future where he was the sole survivor as the Chitauri poured through a portal in the background. Tony's always been sure there was some other attack coming, but he's never known who/when it would arrive, so he was trying to prepare for the eventuality with Ultron. Which didn't quite go like he'd hoped.

At Titan during the battle, Thanos identifies and calls out “ Mr
Stark” to which Tony asks "You know me?" And Thanos responds "You’re
not the only one cursed with knowledge"

I don't have a specific answer for this one, although I've seen a few theories suggesting that controlling the Soul Stone means that he can "know" Tony, although I also think the odds are good that with the Chitauri attack, and the events of Age of Ultron and even Civil War - if Thanos has been paying attention to Earth (and he would as two of the six stones he needs are there) he'd hardly miss reports regarding Iron Man...